Thank you so, so much for sharing. You and CJG seem to be the only two results on the web for extending the _api endpoint. My use case was to be able to create consumable endpoints available both inside SharePoint AND from apps. WCF services under _vti_bin are simple to create, but do not meet the need, and cannot be accessed through the webproxy.

This is an amazing undocumented extension capability for SP2013 on prem. It allows you to "close the gap" between FTC and Apps by offering custom endpoints that are otherwise unavailable via REST/CSOM, and ultimately reduce the overall amount of FTC in the farm.